The present paper proposes a fast numerical method for the linear Volterra integral equations withregular and weakly singular kernels having smooth solutions. This method is based on the approx-imation of the kernel, to simplify the integral operator and then discretization of the simpliedoperator using a forward dierence formula. To analyze and verify the accuracy of the method, weexamine samp...

In the standard approach, particle methods for the Boltzmann equation are obtained using an explicit time discretization of the spatially homogeneous Boltzmann equation. This kind of discretization leads to a restriction on the discretization parameter as well as on the diierential cross section in the case of the general Boltzmann equation. Recently, it was shown, how to construct an implicit ...

Abstract. We consider a parabolic interface problem which models the transport of a dissolved species in two-phase incompressible flow problems. Due to the so-called Henry interface condition the solution is discontinuous across the interface. We use an extended finite element space combined with a method due to Nitsche for the spatial discretization of this problem and derive optimal discretiz...

Problem statement: Handling numerical data stored in a relational database has been performed differently from handling those numerical data stored in a single table due to the multiple occurrences (one-to-many association) of an individual record in the non-target table and non-determinate relations between tables. Numbers in Multi-Relational Data Mining (MRDM) were often discretized, after co...

Investigating nozzle’s orifice flow is challenging both experimentally and theoretically. This paper focuses on simulating flow inside diesel injector nozzle via Ansys fluent v15. Validation is performed with experimental results from Winkhofler et al (2001). Several important parameters such as mass flow rate, velocity profiles and pressure profiles are used for this validation. Results includ...

Abstract. Convergence of a full discretization is shown for a general class of nonlinear parabolic November 10, 2011 problems. The numerical method combines the backward Euler method for the time discretization with a generalized internal approximation scheme for the spatial discretization. The governing monotone elliptic differential operator is described by a nonlinearity that may have anisot...

In this article, we propose optimal discretization of analog filters (or controllers) based on the theory of sampled-data H∞ control. We formulate the discretization problem as minimization of the H∞ norm of the error system between a (delayed) target analog filter and a digital system including an ideal sampler, a zero-order hold, and a digital filter. The problem is reduced to discrete-time H...

There is a tradeoff between speed and accuracy in fitness evaluations when various discretization sizes are used to estimate the fitness. This paper introduces discretization scheduling, which varies the size of the discretization within the GA, and compares this method to using a constant discretization. It will be shown that when scheduling the discretization, less computation time is used wi...

In this article, we propose optimal discretization of analog filters (or controllers) based on the theory of sampleddata H∞ control. We formulate the discretization problem as minimization of the H∞ norm of the error system between a (delayed) target analog filter and a digital system including an ideal sampler, a zero-order hold, and a digital filter. The problem is reduced to discrete-time H∞...